@Su.Ki. - I'll join you in waiting for the experts to pronounce a verdict on this one. :) I confess, I don't much <em>like</em> the idea of "tree" being pronounced as "chree." But when I actually try saying "tree"/"chree" or "train"/"chrain," both pronunciations sound equally correct and native to me. It may be just a transitional "sh" that I'm hearing, though, as you say, between "t" and "r."
As far as I know, there are no minimal pairs, anyway -- in fact I don't think English has any words with the consonant cluster "chr" at all (except words with Greek roots, which are pronounced as "kr").
@ ᑎᗩDᗩ’s eager4 winter - Personally, I pronounce "Tuesday" with a /t/ sound. But I've heard some speakers who do use a soft "ch" sound when they say this word. I assume that this "ch" pronunciation is the pun behind the title of Neil Gaiman's children's book "Chu's Day." (Edit: I just saw your last comment, Benny. If it's the British pronunciation, that makes sense, since Gaiman is British.)